How do I smooth a low-poly mesh without shrinking its volume?
There is actually no need to subdivide mesh before you sculpt.  If you go into sculpt mode with your character selected, you can then select Dyntopo > Enable Dyntopo on the toolbar.



This will automatically subdivide you mesh as needed while you are sculpting.  You can change the Detail Size to a lower number for more detail.



Here is what Dyntopo with a detail size of 3px does to a cube that only had six faces before I started sculpting:



As you can see, with dyntopo enabled, Blender only subdivides the area that is being sculpted, instead of subdividing the whole mesh.